Question

The measure of one angle of a right triangle is 50 more than the measure of the smallest angle. Find the measures

of all three angles.

Short answer

$20°,70°,90°$are the measures of all three angles.

Step-by-step solution

Step 1. Given Information:

The measure of one angle of a right triangle is 50 more than the measure of the smallest angle.

We have to find the measures of all three angles.

Step 2. Name.

Choose a variable to represent it.

$$\begin{gathered} Leta=1^{st}angle. \\ a+50°=2^{nd}angle \\ 90°=3^{rd}angle(therightangle) \end{gathered}$$

Draw the figure and label it with the given information.

Step 3. Translate.

Write the appropriate formula.

$m\angle A+m\angle B+m\angle C=180°$

Substitute into the formula.

$a+(a+50)+90°=180°$

Step 4. Solve the equation.

$$\begin{gathered} a+(a+50°)+90°=180° \\ 2a+140°=180° \\ 2a=180°-140° \\ 2a=40° \\ a=20°firstangle \\ a+50secondangle \\ 20°+50°=70° \\ 90°thirdangle \end{gathered}$$

Step 5. Check

$$\begin{gathered} 20°+70°+90°=180° \\ 180°=180° \end{gathered}$$

verified